Well, for what it's worth, I started the free day and had Raj practice making drinks. He got the first Mixology skill point but had to stop to go to work. He got promoted. So, either it was coincidence (I don't think so) or the game had to see some Mixology skill. Of course, the point for the promotion didn't count because it was a free day!
That's okay, though, because I'm at a point in the challenge where I need to delay points so control of my heir doesn't happen while she is still a child.